Modern machine-learning applications require huge artificial networks demanding computational power and memory. Light-based platforms promise ultrafast and energy-efficient hardware, which may help realize next-generation data processing devices. However, current photonic networks are limited by the number of input-output nodes that can be processed in a single shot. This restricted network capacity prevents their application to relevant large-scale problems such as natural language processing. Here, we realize a photonic processor for supervised learning with a capacity exceeding 1.5 × 10 10 optical nodes, more than one order of magnitude larger than any previous implementation, which enables photonic large-scale text encoding and classification. By exploiting the full three-dimensional structure of the optical field propagating in free space, we overcome the interpolation threshold and reach the over-parameterized region of machine learning, a condition that allows high-performance sentiment analysis with a minimal fraction of training points. Our results provide a novel solution to scale up light-driven computing and open the route to photonic natural language processing.